A similar result holds for the Cover–Efron cones, which are random cones with a different distribution, introduced earlier (see Cover and Efron [1]}). With random vectors \(X_1,\dots ,X_N\)  as above, let \(C_N\)  be the random cone defined as \({\rm pos}\lbrace X_1,\dots ,X_N\rbrace \) , under the condition that this positive hull is different from \({\mathbb {R}}^d\) . The following was proved by Hug and Schneider [2]}. If (REF ) holds, then
\(\lim _{d\rightarrow \infty } \frac{{\mathbb {E}}\,f_k(C_N)}{\binom{N}{k}} =\left\lbrace  \begin{array}{ll} 1 & \mbox{if }\rho <\rho _W(\delta ),\\ 0 & \mbox{if }\rho >\rho _W(\delta ).\end{array}\right.\) 
